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2 years ago

Find two numbers which have a sum of 132 and that can be written as the simplified ratio 3:8

Mathematics

1 answer:

Molodets [167]2 years ago

5 0

Answer:

96 and 36

Step-by-step explanation:

3+8 = 11

132/11 = 12

so:

12 x 3 = 36

12 x 8 = 96

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Which description best fits the distribution of the data shown in the histogram?

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This is an approximately bell-shaped distribution. The highest bar is in the center, with height = 12. Just to its left and right are bars of heights 6 and 5. At the extremes are bars of heights 2 and 1.

If the highest bar was on the left, it would be skewed left (and if it was on the right, skewed right). A uniform distribution would more or less have the same height level over all the bars.

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3 years ago

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Which of the following are the coordinates of the vertex of y = −x2 + 2x + 1? (2, 1) (1, –2) (1, 2) (–2, 1)

IceJOKER [234]

Answer:

Step-by-step explanation:

We want to determine the vertex of the quadratic equation:

$\displaystyle y = -x^2 + 2x + 1$

Recall that the vertex is given by the formulas:

$\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -1, b = 2, and c = 1.

Determine the x-coordinate of the vertex:

$\displaystyle x = -\frac{(2)}{2(-1)} = 1$

To determine the y-coordinate, evaluate the function at x = 1:

$\displaystyle \begin{aligned} y(1)&= -(1)^2 + 2(1) + 1 \\ &= 2\end{aligned}$

In conclusion, the vertex of the quadratic equation is (1, 2).

Hence, our answer is C.

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2 years ago

In the last ten games, Jamal made 7/9 of his free throws and brian made 5/8 of bis free throws. Which player has the better reco

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2 years ago

Which of the values shown are potential roots of f(x) = 3x3 – 13x2 – 3x + 45? Select all that apply.

galina1969 [7]

Answer:

All potential roots are 3,3 and $-\frac{5}{3}$ .

Step-by-step explanation:

Potential roots of the polynomial is all possible roots of f(x).

$f(x)=3x^3-13x^2-3x+45$

Using rational root theorem test. We will find all the possible or potential roots of the polynomial.

p=All the positive/negative factors of 45

q=All the positive/negative factors of 3

$p=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45$

$q=\pm 1,\pm 3$

All possible roots

$\frac{p}{q}=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45,\pm \frac{1}{3},\pm \frac{5}{3}$

Now we check each rational root and see which are possible roots for given function.

$f(1)= 3\times 1^3-13\times 1^2-3\times 1+45\Rightarrow 32\neq 0$

$f(-1)= 3\times (-1)^3-13\times (-1)^2-3\times (-1)+45\Rightarrow \neq 32$

$f(-3)= 3\times (-3)^3-13\times (-3)^2-3\times (-3)+45\Rightarrow \neq -144$

$f(3)= 3\times (3)^3-13\times (3)^2-3\times (3)+45\Rightarrow =0\\\\ \therefore x=3\text{ Potential roots of function}$

Similarly, we will check for all value of p/q and we get

$f(-5/3)=0$

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